Issue |
ESAIM: M2AN
Volume 44, Number 4, July-August 2010
|
|
---|---|---|
Page(s) | 597 - 625 | |
DOI | https://doi.org/10.1051/m2an/2010021 | |
Published online | 17 March 2010 |
The G method for heterogeneous anisotropic diffusion on general meshes
1
IFP,
1 & 4 av. du Bois-Préau,
92852 Rueil-Malmaison Cedex, France.
leo.agelas@ifp.fr; daniele-antonio.di-pietro@ifp.fr
2
Université Montpellier 2,
Institut de Mathématiques et Modélisation de Montpellier,
CC 051,
Place Eugène Bataillon,
34095 Montpellier Cedex 05, France.
droniou@math.univ-montp2.fr
Received:
27
November
2008
In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity, we introduce a non-standard test space in (Ω) and prove its density. Thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with classical multi-point Finite Volume methods is provided.
Mathematics Subject Classification: 65N08 / 65N12
Key words: Finite volume methods / heterogeneous anisotropic diffusion / MPFA / convergence analysis
© EDP Sciences, SMAI, 2010
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